Polymer functionalization of many substrates, including proteins, nanoparticles, solid surfaces, hydrogels, etc., are of crucial importance for their applications. For example, protein-polymer conjugates provided by polymer functionalized proteins have been widely used as therapeutics, such as PEGylated proteins. However, the existing polymer conjugating methods usually produce functionalized substrate with one single polymer chain to be conjugated to the reacting site. To conjugate two or more different individual polymer chains (to form so-called hetero-arm polymers, or star-like polymers each having a core with “arms” of different polymer chains attached to the core) to the same reacting site of substrates are challenging but powerful to make highly functionalized materials with the combined properties of the conjugated polymer chains. For example, two kinds of polymer chains could be conjugated to the same active reacting site of therapeutic proteins, with one chain to prolong the half-lives of the proteins and the other to target the diseased sites. This could potentially increase the drug efficacy significantly. No existing methods for facilely conjugation of multiple different polymer chains to one single reacting site are currently in routine use. The present invention addresses this and other related needs.